# Tagged Questions

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### find all path segments in an undirected graph [closed]

I have an undirected graph, like the following: . C . / \ . B F . / / \ . A D E The edges are: ...
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### Computing the chromatic polynomial of graph modulo $x-3$

The chromatic polynomial of graph $P(G,x)$ is univariate polynomial which counts the number of colorings of $G$ with $x$ colors for natural $x$. Graph is not $k$ colorable iff $P(G,k)=0$. The ...
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### Algorithm to construct metric space endomorphism with controlled square

Given a finite metric space $(M,d)$ with parameters $K \geq 1$ and $\epsilon > 0$, I'd like to algorithmically check for the existence of a non-identity map $\phi:M \to M$ which happens to be ...
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### Algorithms for computing the Resilience of Graphs

The definition of resilience with a graph $G$ w.r.t to a monotone property $\mathcal{P}$ is well known. (Global resilience) Let $\mathcal{P}$ be an increasing monotone property. The global ...
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### Bipartite graph [closed]

First of all, thank you for your time to reading my post. I am a researcher but not a mathematician, i have some difficulties in solving a math problem, that why i am here to ask your help. I just ...
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### A small unavoidable collection of subgraphs

What is the smallest number S(k,n) of unlabeled graphs on k vertices such that every simple graph on n vertices contains at least one of these as an induced subgraph? I'd like to avoid exhaustive ...
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### A problem related to routing in a graph

I have come across a new problem - I want to know whether this problem is similar to some existing problem or not. The new problem is this. There is a tourist who has a having the following ...
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### Is undirected short-simple-path-through-3-vertices decidable in polynomial time?

Consider the following language: $L=\{\langle G=(V,E),s,v,t,l\rangle\;|\;s,v,t\in V, l\in \mathbb{N} \wedge$ There exists a simple path from $s$ to $t$, going through $v$ of length $\leq l\}$. ($G$ ...
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### Determine if a graph has a large clique

This question is quite specific and practical. I hope it is still relevant for MO and will not be removed. I have a collection $\mathcal{C}$ of graphs having from 5000-6000 vertices and edge density ...
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### Smallest distribution of points with genuinely different clusterings

An hierarchical clustering algorithm for (finite) sets of points in a given metric space is essentially determined by its linkage criterion, which defines the distance between arbitrary (finite) sets ...
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### Details of generation programs supplied with nauty

The program nauty comes with gtools which contains, among others, several generation programs like geng, genbg, ... I was ...
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### Counting simple 4-cycles in an undirected graph [closed]

I'm looking for an algorithm which just counts the number of simple and distinct 4-cycles in an undirected graph labelled with integer keys. I don't need it to be optimal because I only have to use it ...
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### Uniformly sampling from the set of all simplicial maps

Let $K$ and $L$ be finite simplicial complexes that remain fixed throughout. How does one efficiently sample (according to the uniform distribution) elements from the finite set of simplicial ...
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### Efficient isomorphic subgraph matching with similarity scores

I'm a computer vision PhD student, and I'm looking for an efficient approximation to the following problem, which could end up helping in image to image matching. Failing that, pointers to relevant ...
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### Minimum cut in near complete graph

I have a problem with an algorithm that i don't quite understand. The mathematics are not the problem, but I don't understand how it can work in practice. The problem is in the paper ...
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### Efficient Hamiltonian cycle algorithms for graph classes

Generally speaking finding a Hamiltonian cycle is NP-Hard and so tough. But if $G=L(H)$ is the line graph of $G$ then we can reduce the finding of a Hamiltonian cycle in $G$ to a Eurler your of $H$ ...
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### Can one measure the infeasibility of four color proofs?

Terms like "impractical" and "unfeasible" are used to say the Robertson, Sanders, Seymour, and Thomas proof of the four color theorem needs computer assistance. Obviously no precise measure is ...
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### Generating k-partite graphs

Does there exist an efficient algorithm for generating all non-isomorphic k-partite graphs up to a certain order $n$? I've read through the nauty tutorial, but it doesn't look like anything beyond ...
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### Geodesics in Graphs:Shortest Paths vs Going as Straight Ahead as Possible

According to Wikipedia http://en.wikipedia.org/wiki/Geodesic, a geodesic " is a generalization of the notion of a "straight line" to "curved spaces " and further " In the presence of an affine ...
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### Estimate size of graph by taking random walks

Let $G$ be a connected, finite graph and let $v_0$ be a vertex of $G$. I'm interested in methods of estimating the number of vertices in $G$, based on local exploration only. What I have in mind is: ...
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### Rough structure of the double coset space/Graph bijections up to automorphisms

I am dealing with bijective maps $\pi:\Gamma_1\to \Gamma_2$ between two graphs with the same number of vertices $N=O(10)$. The graphs have a significant automorphism group (these are disconnected ...
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### Reference Request for: Finding Large Bipartite Subgraphs via Destruction of Odd Cycles in Graphs

From the observation, that a bipartite graph doesn't contain odd cycles, it would seem natural to attempt to destroy all odd cycles in the most efficient way, by either removing edges or vertices of ...
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I am seeking some reference on already existing work for the following problem. Given an $n$-dimensional square matrix $A=DP$ where $D$ is a diagonal and $P$ is a permutation matrix (think of Gaussian ...
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### What algorithms do you know for beltway reconstruction?

I've faced the beltway reconstruction problem and I've developed a simple backtrack algorithm, what algorithms do you know for this problem? Beltway Reconstruction Problem: Assume there is a set of ...
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### Strategic vertex labeling

We are given a graph $G=(V,E)$ with positive edge weights $w_{i}$ and numerical {0,1,-1} labels $l$ for all vertices . We know that $G$ has a subset $G'$ with all vertices labeled 0(all vertices with ...
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### How quickly can we test if a graph is distance-regular?

A (simple, finite, connected) graph $G$ is distance regular if there exist integers $b_i,c_i,i=0,...,D$ such that for any two vertices $x,y$ in $G$ and distance $i=d(x,y)$, there are exactly $c_i$ ...
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### Separation of Anti-Hole Inequality

Given an undirected graph $G=(V,E)$ with no loops or multiple edges, a stable set is a set of vertices for which no two vertices are adjacent. An induced subgraph $H$ of $G$ is called an odd-antihole ...
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### regular hyper graph construction

Is there any algorithm to generate 3-uniform k-regular hypergraph with n vertices?? Any help is appreciated. Thanks.
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### Removing cycles from an undirected connected bipartite graph in a special manner

Consider an undirected connected bipartite graph (with cycles) $G = (V_1,V_2,E)$, where $V_1,V_2$ are the two node sets and $E$ is the set of edges connecting nodes in $V_1$ to those in $V_2$. We ...
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### algorithmic almost equitable partitioning

Let $G$ be a graph -- possibly infinite, but I will be glad to learn a positive result even in the finite case. Then the trivial partition (i.e., one cell coinciding with the whole $G$) is clearly ...
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### Algorithm to solve Sokoban-like game on graphs - move chips from one set of vertices to another

The question is close to the Sokoban game (thanks to Dima Pasechnik !), but a little different in details. Consider a directed graph (multi-graph). Consider some set of marked chips (chip1, ...
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### Toroidality testing

Is there a standard test for the recognition of toroidal graphs? I have been using the Boyer-Myrvold algorithm (which has a MATLAB implementation) and would like to know if there is something ...
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### Generating non-isomorphic graphs by adding edges to a given graph

Hello! This question is in a way related to the one I posted on math.se. Since the question there did not produce any final answer I am trying my luck here! I am given a fairly large graph $G$ and ...
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### Search for common substructures in list of graphs

I have had the following problem on several occasions and I was wondering whether there is a general technique to solve this problem. Given a list of graphs with property $P$. Is there a general ...
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### Is it possible to decide in polynomial time if a poset is a subposet of another which is given ?

I am reading some theory on partial orders and I wonder something which perhaps has a simple answer : Given two partial orders $G_1,G_2$ (by their hasse diagrams), is it possible to know in ...
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### Finding the lowest cost set of disjoint paths using all nodes in a directed graph?

I have a directed graph with edges connecting nodes representing costs. I wish to find the set of paths which -go from node 'start' to node 'end' -are node-disjoint (except for the start and end ...
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### Need input on a potentially NP-hard maximal edge-weighted multi-cycle graph

I've posted a question on Stack Overflow regarding a seemingly NP-hard problem on maximization of weighted cycles in a graph problem. One of the respondents cited Professor David Speyer's Math ...
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### An MST-like problem with vertex selection

Consider a planar pointset in a rectangle, where every point has a color (an integer label). We need to select one point of every color, so as to minimize the cost of a planar MST of selected points ...
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### Is Logical Min-Cut Problem, NP-Complete?

Logical Min Cut (LMC) Problem: Suppose that G = (V, E) is an unweighted digraph, s,t are two vertices of V, and t is reachable from s. LMC Problem states that how we can make t unreachable from s by ...